Abstract
In this paper, we prove that planar graphs without { 4 , 6 , 7 } -cycles and without two 5-cycles sharing exactly one edge are 3-colorable. This improves the result in [O.V. Borodin, A.N. Glebov, A. Raspaud, M.R. Salavatipour, Planar graphs without cycles of length from 4 to 7 are 3-colorable, J. Combin. Theory Ser. B 93 (2005) 303–311].
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